Methods & Tests: Cox proportional hazards model

Cox proportional hazards model: A regression method described by D.R. Cox (J Royal Stat Soc Series B 1972;34:187-220; JSTOR-UK) for modeling survival times (for significance of the difference between survival times log-rank test is used). It is also called proportional hazards model because it estimates the ratio of the risks (hazard ratio or relative hazard). As in any regression model there are multiple predictor variables (such as prognostic markers whose individual contribution to the outcome is being assessed in the presence of the others) and the outcome variable (e.g. whether the patients survived five years or died during follow-up etc). The model assumes that the underlying hazard rate (rather than survival time) is a function of the independent variables and consistent over time (proportionality assumption i.e. the survival functions of the groups are approximately parallel). There is no assumption for the shape and nature of the underlying survival function. Cox’s regression model has been the most widely used method in survival data analysis regardless of whether the survival time is discrete or continuous and whether there is censoring (Lee & Go 1997). Cox regression uses the maximum likelihood method rather than the least squares method (Online Cox Proportional Hazards Survival Regression; a Superlectures on survival analysis; Cox’s proportional hazards model; an example of Model Building).